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| ************* | ||
| signrank() | ||
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| Description | ||
| =========== | ||
| Conducts the Wilcoxon signed-ranks test for paired-sample data. Data can be entered using the formula_like structure, | ||
| or by passing two array like structures. How to use both of these approaches will be | ||
| demonstrated. The results can be returned as Pandas DataFrame object (default) or as a Python | ||
| dictionary object. | ||
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| The data model is passed to *signrank* and then the *conduct* method needs to be applied. This | ||
| method returns 3 data objects within a tuple. | ||
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| Parameters | ||
| ========== | ||
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| Input | ||
| ----- | ||
| **signrank(formula_like = None, data = {}, group1 = None, group2 = None, zero_method = "pratt", correction = False, mode = "auto")** | ||
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| * **formula_like** : A valid formula which will parse the data into a design matrix. | ||
| * **data** : The dataframe which contains the data to be analyzed; required if using *formula_like*. | ||
| * **group1** : The array like object which contains data for the paired-sample. | ||
| * **group2** : The array like object which contains data for the paired-sample. | ||
| * **zero_method** : How to handle the zero-differences in the ranking process. Available options are (from :cite:`scipy_wilcoxon`): | ||
| * *"pratt"* : Includes zero-differences in the ranking process, but drops the ranks of the zeros (default). | ||
| * *"wilcox"* : Discards all zero-differences. | ||
| * **correction** : Boolean value indicating if the continuity correction should be applied; see :cite:`scipy_wilcoxon` for more information. | ||
| * **mode** : Method to calculate the p-value, see :cite:`scipy_wilcoxon` for more information. Options are: | ||
| * *"auto"* : Use the exact distribution if there are no more than 25 observations and no ties, otherwise a normal approximation will be used (default). | ||
| * *"exact"* : Use the exact distribution, can be used if there are no more than 25 observations and no ties. | ||
| * *"approx"* : Use a normal approximation. | ||
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| Returns | ||
| ------- | ||
| Returns an object with class "signrank"; this object has an accessible method which is described below. | ||
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| signrank methods | ||
| ^^^^^^^^^^^^^^^^ | ||
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| * **conduct(return_type = "Dataframe", effect_size = [])** | ||
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| * **return_type** : The type of data structure the results should be returned as. Supported options are 'Dataframe' which will return a Pandas DataFrame or 'Dictionary' which will return a dictionary. | ||
| * **effect_size** : A list object which indicates which effect size measures should be calculated. Available options are: | ||
| * *pd* : Calculates the Rank-Biserial r coefficient. | ||
| * *pearson* : Calculates the Pearson r coefficient. | ||
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| After using the conduct method three objects will be returned within a tuple. The first object | ||
| provides descriptive information regarding the ranks, the second object contains the adjustment information, | ||
| and the third object contains the test results. | ||
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| Effect size measures formulas | ||
| ============================= | ||
| By default no effect size measures are calculated. | ||
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| Rank-Biserial r :cite:`Kerby2012` | ||
| """""""""""""""""""""""""""""""""""""""""""""""" | ||
| .. math:: | ||
| \text{Rank-Biserial r = } \frac{\sum{Ranks}_{+} - \sum{Ranks}_{-}}{\sum{Ranks}_{total}} | ||
| Pearson r :cite:`Fritz_Morris_Richler2012` | ||
| """""""""""""""""""""""""""""""""""""""""" | ||
| .. math:: | ||
| \text{Pearson r = } \frac{Z}{\sqrt{N}} | ||
| Where N is the total number of observations included in the model. | ||
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| Examples | ||
| ======== | ||
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| Loading Packages and Data | ||
| ------------------------- | ||
| First to load required libraries for this example. Below, an example data set will be loaded | ||
| in using statsmodels.datasets; the data loaded in is a data set available through Stata | ||
| called 'fuel'. | ||
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| .. code:: python | ||
| import researchpy as rp | ||
| import pandas as pd | ||
| # Used to load example data # | ||
| import statsmodels.datasets | ||
| fuel = statsmodels.datasets.webuse('fuel') | ||
| fuel["id"] = range(1, fuel.shape[0] + 1) | ||
| fuel.info() | ||
| .. raw:: html | ||
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| <table border="1" class="dataframe"> <thead> <tr style="text-align: right;"> <th>mpg1</th> <th>mpg2</th> <th>id</th> </tr> </thead> <tbody> <tr> <td>20.0000</td> <td>24.0000</td> <td>1</td> </tr> <tr> <td>23.0000</td> <td>25.0000</td> <td>2</td> </tr> <tr> <td>21.0000</td> <td>21.0000</td> <td>3</td> </tr> <tr> <td>25.0000</td> <td>22.0000</td> <td>4</td> </tr> <tr> <td>18.0000</td> <td>23.0000</td> <td>5</td> </tr> </tbody></table> | ||
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| The data is currently in a wide structure where each column, mpg1 and mpg2, represent a value for the same ID. This format | ||
| is supported by signrank. The long format structure is also supported using the *formula_like* approach, in order to have | ||
| the data ready for this demonstration section the transformation will be conducted here. | ||
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| .. code:: python | ||
| fuel2 = pandas.melt(fuel, id_vars = "id", | ||
| value_vars = ["mpg1", "mpg2"], | ||
| var_name = "mpg") | ||
| fuel2.head() | ||
| .. raw:: html | ||
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| <table border="1" class="dataframe"> <thead> <tr style="text-align: right;"> <th>id</th> <th>mpg</th> <th>value</th> </tr> </thead> <tbody> <tr> <td>1</td> <td>mpg1</td> <td>20.0000</td> </tr> <tr> <td>2</td> <td>mpg1</td> <td>23.0000</td> </tr> <tr> <td>3</td> <td>mpg1</td> <td>21.0000</td> </tr> <tr> <td>4</td> <td>mpg1</td> <td>25.0000</td> </tr> <tr> <td>5</td> <td>mpg1</td> <td>18.0000</td> </tr> </tbody></table> | ||
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| Signrank using Wide Structure Datasets | ||
| --------------------------------------- | ||
| Since the test returns 3 data objects, this demonstration will assign each data object to variable. This is not required, but | ||
| it makes the output look cleaner. | ||
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| .. code:: python | ||
| desc, var_adj, res = signrank(group1 = fuel.mpg1, group2 = fuel.mpg2).conduct() | ||
| print(desc, var_adj, res, sep = "\n"*2) | ||
| .. raw:: html | ||
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| <table border="1" class="dataframe"> <thead> <tr style="text-align: right;"> <th>sign</th> <th>obs</th> <th>sum ranks</th> <th>expected</th> </tr> </thead> <tbody> <tr> <td>positive</td> <td>3</td> <td>13.5000</td> <td>38.5000</td> </tr> <tr> <td>negative</td> <td>8</td> <td>63.5000</td> <td>38.5000</td> </tr> <tr> <td>zero</td> <td>1</td> <td>1.0000</td> <td>1.0000</td> </tr> <tr> <td>all</td> <td>12</td> <td>78.0000</td> <td>78.0000</td> </tr> </tbody></table> | ||
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| <table border="1" class="dataframe"> <thead> <tr style="text-align: right;"> <th>unadjusted variance</th> <th>adjustment for ties</th> <th>adjustment for zeros</th> <th>adjusted variance</th> </tr> </thead> <tbody> <tr> <td>162.5000</td> <td>-1.6250</td> <td>-0.2500</td> <td>160.6250</td> </tr> </tbody></table> | ||
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| <table border="1" class="dataframe"> <thead> <tr style="text-align: right;"> <th>z</th> <th>w</th> <th>pval</th> </tr> </thead> <tbody> <tr> <td>-1.9726</td> <td>13.5000</td> <td>0.0485</td> </tr> </tbody></table> | ||
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| If one does not assign each object to a variable, the output is still readable. | ||
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| .. code:: python | ||
| signrank(group1 = fuel.mpg1, group2 = fuel.mpg2).conduct() | ||
| .. raw:: literal |
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